L04-4up

# L04-4up - Synthesis of Combinational Logic A Functional...

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L04 - Logic Synthesis 1 6.004 – Fal 2010 9/21/10 Synthesis of Combinational Logic Lab 1 is due Thursday Quiz 1 is this Friday (in section) A B L04 - Logic Synthesis 2 6.004 – Fal 2010 9/21/10 Functional Speci±cations There are many ways of specifying the function of a combinational device, for example: A B Y If C is 1 then copy B to Y, otherwise copy A to Y C Concise alternatives: truth tables are a concise description of the combinational system’s function. Boolean expressions form an algebra in whose operations are AND (multiplication), OR (addition), and inversion (overbar). Any combinational (Boolean) function can be speciFed as a truth table or an equivalent sum-of-products Boolean expression! Argh… I’m tired of word games C B A Y 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Truth Table CBA A CB BA C A B C Y + + + = L04 - Logic Synthesis 3 6.004 – Fal 2010 9/21/10 Here’s a Design Approach 1) Write out our functional spec as a truth table 2) Write down a Boolean expression with terms covering each ‘1’ in the output: 3) Wire up the gates, call it a day, and declare success! This approach will always give us Boolean expressions in a particular form: SUM-OF-PRODUCTS C B A Y 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Truth Table -it’s systematic! -it works! -it’s easy! -are we done yet??? CBA A CB BA C A B C Y + + + = L04 - Logic Synthesis 4 6.004 – Fal 2010 9/21/10 Straightforward Synthesis We can implement SUM-OF-PRODUCTS with just three levels of logic. INVERTERS/AND/OR Propagation delay -- No more than 3 gate delays (assuming gates with an arbitrary number of inputs) A B C A B C A B C A B C Y

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L04 - Logic Synthesis 5 6.004 – Fal 2010 9/21/10 Basic Gate Repertoire Are we sure we have all the gates we need? Just how many two-input gates are there? AB Y 00 0 01 0 10 0 11 1 AND AB Y 00 0 01 1 10 1 11 1 OR AB Y 00 1 01 1 10 1 11 0 NAND AB Y 00 1 01 0 10 0 11 0 NOR SURGE 2 = 2 4 = 16 2 2 Hmmmm… all of these have 2-inputs (no surprise) … each with 4 combinations, giving 2 2 output cases How many ways are there of assigning 4 outputs? ________________ L04 - Logic Synthesis 6 6.004 – Fal 2010 9/21/10 There are only so many gates There are only 16 possible 2-input gates … some we know already, others are just silly I N P U T AB Z E R O A N D A > B A B > A B X O R O R N O R X N O R N O T ‘B’ A <= B N O T ‘A’ B <= A N A N D O N E 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 01 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 10 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 11 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 How many of these gates can be implemented using a single CMOS gate?
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L04-4up - Synthesis of Combinational Logic A Functional...

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